Since you asked for Bash:
INET_NTOA() { 
    local IFS=. num quad ip e
    num=$1
    for e in 3 2 1
    do
        (( quad = 256 ** e))
        (( ip[3-e] = num / quad ))
        (( num = num % quad ))
    done
    ip[3]=$num
    echo "${ip[*]}"
}
INET_ATON ()
{
    local IFS=. ip num e
    ip=($1)
    for e in 3 2 1
    do
        (( num += ip[3-e] * 256 ** e ))
    done
    (( num += ip[3] ))
    echo "$num"
}
Examples:
$ INET_ATON 10.2.1.255
167903743
$ INET_NTOA 167903743
10.2.1.255
Here is a version that will work in any of the Bourne-derived shells I tried including dash, ksh, several versions of Bash, BusyBox ash, zsh (with -y) and even the Heirloom Bourne Shell.
INET_NTOA() {
    num=$1
    ip=
    for e in 3 2 1
    do
        quad=`echo "256 ^ $e" | bc`
        if [ -n "$ip" ]
        then
            ip=$ip.
        fi
        ip=$ip`echo "$num / $quad" | bc`
        num=`echo "$num % $quad" | bc`
    done
    ip=$ip.$num
    echo "$ip"
}
INET_ATON ()
{
    num=0
    e=3
    saveIFS=$IFS
    IFS=.
    set -- $1
    IFS=$saveIFS
    for ip in "$@"
    do
        num=`echo "$num + $ip * 256 ^ $e" | bc`
        e=`echo "$e - 1" | bc`
    done
    echo "$num"
}